Question

A contractor has at most $42 to spend on nails for a project. Finishing nails cost $0.45 per pound and

common nails cost $0.60 per pound. He would like to purchase at least 30 pounds of nails total.
a. Write a system of linear inequalities:
b. Write two possible solutions:

Answer 1

To write a system of linear inequalities, define the variables as the pounds of finishing and common nails. Then, write the inequalities based on the given conditions. Two possible solutions are x = 10, y = 20 and x = 15, y = 15.

Step-by-step explanation:

To write a system of linear inequalities, let's define the variables:

x = number of pounds of finishing nails

y = number of pounds of common nails

Now we can write the inequalities:

x + y >= 30 (we want to purchase at least 30 pounds of nails)

0.45x + 0.60y <= 42 (we have a budget of $42)

Next, let's find two possible solutions:

One possible solution is x = 10 and y = 20. This satisfies both inequalities and the total pounds of nails is 30.

Another possible solution is x = 15 and y = 15. This also satisfies both inequalities and the total pounds of nails is 30.